Analytical solution of optimal trajectory-shaping guidance

This paper presents a combined midcourse and terminal guidance law design for missiles to achieve range enhancement with excellent intercept performance. We derive analytic solutions of a closed-loop, nonlinear optimal guidance law for three-dimensional flight for both the midcourse and terminal phases. This combined guidance law can quickly modify the missile trajectory during midcourse guidance when the target direction changes. Zero heading error is achieved at handover from the midcourse to the terminal phase. The guidance algorithm is in a feedback form, either in inertial coordinates or in seeker coordinates. It is sufficiently simple for onboard implementation and has been applied successfully for on-line operation.